Question

according to the inverse-square law, if distance between two objects doubles, the force of gravity becomes: a) four times greater b) twice as great c) half as strong d) one-fourth as strong

Explanation:

The inverse - square law for gravitational force is given by \(F = G\frac{m_1m_2}{r^2}\), where \(F\) is the gravitational force, \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between them. Let the initial distance be \(r_1\) and the initial force be \(F_1=G\frac{m_1m_2}{r_1^2}\). If the distance doubles, the new distance \(r_2 = 2r_1\). The new force \(F_2=G\frac{m_1m_2}{r_2^2}=G\frac{m_1m_2}{(2r_1)^2}=G\frac{m_1m_2}{4r_1^2}=\frac{1}{4}\times G\frac{m_1m_2}{r_1^2}=\frac{1}{4}F_1\). So when the distance between two objects doubles, the gravitational force becomes one - fourth as strong.

Answer:

D) One - fourth as strong